基于规模约束聚类的复杂网络划分
Partitioning Complex Networks via Size-constrained Clustering
摘要：
在实践中，最常用的方法来解决图划分问题是多层次的方法。在粗化阶段期间，多级图划分算法通过迭代地收缩节点和边来减小图的大小，直到图足够小以被某个其他算法划分为止。然后，通过连续地将解转移到下一个更精细的图并应用局部搜索算法来改进当前解来构造输入图的分区。在本文中，我们描述了一种新的方法来有效地划分图，特别是如果网络具有高度不规则的结构。更确切地说，我们的算法提供了图形粗化迭代收缩使用标签传播算法计算的大小受限的聚类。提供大小受限聚类的相同算法也可以在粗化期间用作快速且简单的局部搜索算法。根据算法的配置，我们能够计算出性能优于所有竞争对手的非常高质量的分区，或者在质量方面与最佳竞争对手hMetis相当的分区，同时平均快了近一个数量级。最快的配置使用一台机器在大约10分钟内分割出我们可用的最大图，其中有33亿条边，而切割的边不到最快的竞争对手kMetis的一半。
英文摘要：
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis.
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